Open Access

A characterization of chaotic order

Journal of Inequalities and Applications20062006:79123

DOI: 10.1155/JIA/2006/79123

Received: 15 November 2005

Accepted: 4 January 2006

Published: 8 June 2006


The chaotic order among positive invertible operators on a Hilbert space is introduced by . Using Uchiyama's method and Furuta's Kantorovich-type inequality, we will point out that if and only if holds for any , where is any fixed positive number. On the other hand, for any fixed , we also show that there exist positive invertible operators , such that holds for any , but is not valid.


Authors’ Affiliations

Department of Mathematics, Henan Normal University


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© C. Yang and F. Gao 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.